Interdisciplinary Applied Mathematics

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In Chapter 11 we focus on water and its properties in various forms; this is one of the most actively investigated areas because of its importance in nature. The anomalies that exist in the bulk properties of water make it very interesting and challenging for research, and a vast deal of literature is already available. Even though water has been studied for more than 100 years now, its properties are far from understood. With the advances in fabrication of nanochannels that are only a few molecular diameters in critical dimension, the properties of water in confined nanochannels have recently received a great deal of attention. In this chapter, after introducing some definitions and atomistic models for water, we present the static and dynamic behavior of water in confined nanochannels.

In Chapter 12 we discuss the fundamentals and simulation of electroosmotic flow in nanochannels. The basic theory was covered in Chapter 7, so here the limitations of the continuum theory for electroosmotic flow in nanochannels are identified by presenting a detailed comparison between continuum and MD simulations. Specifically, the significance of the finite size of the ions and the discrete nature of the solvent molecules are highlighted. A slip boundary condition that can be used in the hydrodynamic theory for nanochannel electroosmotic flows is presented. Finally, the physical mechanisms that lead to the charge inversion and flow reversal phenomena in nanochannel electroosmotic flows are discussed.

In Chapter 13 we focus on functional fluids and on functionalized devices, specifically nanotubes. The possibility to target and precisely control the electrooptical as well as the mechanical properties of microstructures in a dynamic way using external fields has opened new horizons in microfluidics research including new concepts and protocols for micro- and nanofabrication. On the more fundamental level, systematic studies of paramagnetic particles or charged particles and their dynamics offer insight into the role of Brownian noise in microsystems as well as conceptual differences between deterministic and stochastic modeling. This is studied in the first part of this chapter. In the second part of the chapter we study carbon nanotubes and their properties. Carbon nanotubes with diameters as small as 5-10 A are comparable to the diameters encountered in biological ion channels. By functionalizing carbon nanotubes, it is possible to tune the surface properties of carbon nanotubes to investigate the function of a variety of ion channels. To enable such advances, it is important to understand how water, ions, and various electrolytes interact with carbon nanotubes and functionalized nanotubes.

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